Answer to Question #296246 in Geometry for Miella

Question

A doctors office provides water coolers with cone- shaped paper cups. A cup has a diameter of 2.5 in., and the distance from the tip of the cone to the lip is 4in. What is the height of the cup? What is the volume of the cup? Round you answers to the nearest tenth.

Answer 1

$$r=2.5\ in./2=1.25\ in.$$

$$h=\sqrt{l^2-r^2}=\sqrt{(4\ in.)^2-(1.25\ in.)^2}\approx3.8\ in.$$

The height of the cup is $3.8\ in.$

$$V=\dfrac{\pi r^2 h}{3}=\dfrac{\pi (1.25\ in.)^2\sqrt{(4\ in.)^2-(1.25\ in.)^2} }{3}$$

$$\approx6.2\ in.^3$$

The volume of the cup is 6.2 cubic inches.